CASE STUDY SUMMARY
This case study solves sparse reconstruction problems from SPARCO toolbox using External Functions Tool of PSG and operator given by SPARCO toolbox for implicit working with matrices.
SPARCO is a suite of problems for testing and benchmarking algorithms for sparse signal reconstruction, Berg et al. (2007, 2008). It is also an environment for creating new test problems. Also a suite of standard linear operators is provided from which new problems can be assembled. SPARCO is implemented entirely in MATLABand is self contained.
Problems included in the SPARCO toolbox were initially considered by different authors in different application areas: imaging, compressed sensing, geophysics, information compressing, etc. Relevant references can be found in the SPARCO toolbox.
The objective of Sparse Reconstruction is to find a decision vector which has a small number of non-zero components and satisfies exactly or almost exactly a system of linear equations. There are many variants of optimization formulations of such problems. These formulations are described in paper Boyko et al. (2011).
We solved problems included in SPARCO toolbox in so called “LASSO-O” formulation. “LASSO-O” minimizes L2-error of regression with adding to objective a regularization linear term which is equal to the sum of absolute values of variables. The regularization term is intended to “suppress" components with small values. To investigate property of solution we solved every problem with different weight of regularization linear term and calculated cardinality and max functions in optimal points. These problems can be easy solved by methods for unconstrained optimization.
SPARCO toolbox provides a set of operators to deal with data. Problems were solved in PSG MATLAB Environment with the PSG External Function subroutine to avoid generating full matrix and to save time and memory.
We reported performance of AORDA Portfolio Safeguard (PSG) 64 bit version conducted on PC with 2.83 MHz processor.

In the problem formulations we have included several "dummy" functions multiplied by 0 (zero). Such "dummy" functions do not not impact solution process, but values of these functions are printed in the final solution file.

For instance, you can view many "dummy" functions in the following problem formulation: